If various types of gases used for, for example, semiconductor manufacturing are to be supplied to a semiconductor manufacturing device, mass flow controllers are provided on supply channels corresponding to the gases so as to regulate flow rates of the gases, respectively. Conventionally, a pressure regulator is attached to each mass flow controller in series so as to prevent extreme change in an internal pressure of the supply channel of each mass flow controller, thereby simplifying flow rate control.
Flow rate control of each of the mass flow controllers is basically PID control. As a mass flow controller of this type, there is known a mass flow controller exercising a feedback control by changing over PID coefficients between a transitional response state and a stable state, as disclosed in, for example, Patent document 1.
Specifically, the mass flow controller disclosed in Patent document 1 uses values obtained by assigning a flow rate set value to a predetermined function as gain values, respectively by which a deviation is multiplied in proportional operation. For example, a lower value is obtained by the predetermined function used in the stable state if the assigned flow rate set value is lower. That is, the conventional mass flow controller disclosed in Patent document 1 only changes a proportional coefficient, an integral coefficient, and a derivative coefficient (which coefficients will be also referred to as “PID coefficients”, hereinafter) by making the PID coefficients only in proportion to the flow rate set value.
However, the inventor of the present application obtained the following experimental result. In the stable state, optimum PID coefficients differ between a time a primary pressure rises and a time the primary pressure falls. Even if a time change amount of the primary pressure is the same, the PID coefficients differ as long as the primary pressure before change differs. Furthermore, a linear relation is not held among the flow rate set value and the optimum PID coefficient values. As a result, the inventor discovered that there is a limit to improvement in PI (Pressure Insensitive) performance only by making the PID coefficients in proportion to the flow rate set value in the stable state.    Patent document 1: Japanese Unexamined Patent Publication No. 2007-34550